The stream API is part of the HTMLDeviceElement API. This is not yet implemented in any released browser (January 2011).
The stream is served by a client computer. This is theoretically a โserverlessโ solution, because it means that the client-side API can expose client devices (webcams, USB devices, etc.). You can use JavaScript to send the stream to the server if you want.
Since there are no released implementations (with the exception of WebKit nightly codes, it seems), this specification is really not ready for use.
You can always try the nightly build of WebKit and see if your demo works for you. Since this has not yet been released, I do not expect something to work very well. I tried to run last night (WebKit-r74232) and it seems that HTMLDeviceElement is not currently enabled.
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